Schrödinger operators with empty singularly continuous spectra

Let H be a semibounded perturbation of the Laplacian H0in L2(ℝd). For an admissible function φ sufficient conditions are given for the completeness of the scattering system {φ(H), φ(H0)}. If φ is the exponential function and if e-λH is an integral operator we denote the kernel of the difference Dλ = e-λH -e-λH0 by Dλ(x, y), λ > 0. The singularly continuous spectrum of H is empty if ∫ℝd dx ∫ℝd dy|Dλ(X,y)\(1 + |y|2)α < ∞ for some α > 1. This result is applied to potential perturbations and to perturbations by imposing Dirichlet boundary conditions. © 1999 Kluwer Academic Publishers.